11 citations · 61 across the 18 of their papers we have counts for
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Skew Howe duality and q-Krawtchouk polynomial ensemble
Anton Nazarov, Pavel Nikitin, Daniil Sarafannikov
We consider the decomposition into irreducible components of the exterior algebra regarded as a $GL_{n…
Skew Howe duality and limit shapes of Young diagrams
Anton Nazarov, Olga Postnova, Travis Scrimshaw
We consider the skew Howe duality for the action of certain dual pairs of Lie groups on the exterior algebra as a pr…
Limit shape for infinite rank limit of tensor power decomposition for Lie algebras of series so(2n+1)
Anton Nazarov, Pavel Nikitin, Olga Postnova
We consider the Plancherel measure on irreducible components of tensor powers of the spinor representation of so(2n+1). The irreducible representations correspond to the generalize…
Probability measure near the boundary of tensor power decomposition for so(2n+1)
Anton Nazarov, Viktoria Chizhikova
Character measure is a probability measure on irreducible representations of a semisimple Lie algebra. It appears from the decomposition into irreducibles of tensor power of a fund…
Limit shape of probability measure on tensor product of algebra modules
Anton Nazarov, Olga Postnova
We study a probability measure on integral dominant weights in the decomposition of -th tensor power of spinor representation of the Lie algebra . The probability of t…
Splints of root systems for special Lie subalgebras
Vladimir Lyakhovsky, Anton Nazarov, Polina Kakin
Splint is a decomposition of root system into union of root systems. Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive…
On affine extension of splint root systems
Vladimir Laykhovsky, Anton Nazarov
Splint of root system of simple Lie algebra appears naturally in the study of (regular) embeddings of reductive subalgebras. It can be used to derive branching rules. Application o…
Fan, splint and branching rules
Vladimir Laykhovsky, Anton Nazarov
Splint of root system for simple Lie algebra appears naturally in studies of (regular) embeddings of reductive subalgebras. Splint can be used to construct branching rules. We demo…
Affine.m - Mathematica package for computations in representation theory of finite-dimensional and affine Lie algebras
Anton Nazarov
In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms…
Recursive properties of branching and BGG resolution
Vladimir Lyakhovsky, Anton Nazarov
Recurrent relations for branching coefficients are based on a special type of singular element decomposition. We show that this decomposition can be used to construct the parabolic…
Recursive algorithm and branching for nonmaximal embeddings
Vladimir Lyakhovsky, Anton Nazarov
Recurrent relations for branching coefficients in affine Lie algebras integrable highest weight modules are studied. The decomposition algorithm based on the injection fan techniqu…